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The formatted source code for this file is here.
And a raw version here.
Previous work by Youngser Park can be found here.

We now have the following data sets:

featF0: The feature vector looking only at the integrated brightness features.
fs: The feature vector scaled between \([0,1000]\).
logF0: The feature vector, with 0’s removed, then \(log_{10}\) is applied.
slogF0: The feature vector, with 0’s removed, then \(log_{10}\), then scaled by subtracting the mean and dividing by the sample standard deviation.

1 Kernel Density Estimates of the marginals

df1 <- melt(as.matrix(fs))
names(df1) <- c("ind","channel","value")
df1$type <- factor(rep(ffchannel,each=dim(fs)[1]),levels=levels(ffchannel))

lvo <- c(1:5,7:10,19,22,11:16,6,17,18,20,21,23,24)
levels(df1$channel)<-levels(df1$channel)[lvo]

ts <- 22

gg1 <- ggplot(df1, aes(x=value)) + 
    scale_color_manual(values=ccol[lvo]) +
    scale_fill_manual(values=ccol[lvo]) +
    geom_histogram(aes(y=..density..,group=channel,colour=channel),bins=100) +
    geom_density(aes(group=channel, color=channel),size=1.5) +
    facet_wrap( ~ channel, scale='free', ncol=6) +
    theme(plot.title=element_text(size=ts),
          axis.title.x=element_text(size=ts),
          axis.title.y=element_text(size=ts),
          legend.title=element_text(size=ts),
          legend.text=element_text(size=ts-2),
          axis.text=element_text(size=ts-2),
          strip.text=element_text(size=ts), 
          legend.position='none')+
    ggtitle("Kernel Density Estimates of `fs` data.")

print(gg1)

**Figure 1: Kernel density estimates for each channel, on `fs` data.**

2 Level 0

dat <- fs

2.1 Heat maps (Lv 0):

## Formatting data for heatmap
aggp <- apply(dat, 2, mean)
aggp <- t(cbind(aggp, aggp))

The following are heatmaps generated from clustering via K-means++ (at level 1)

heatmap.2(as.matrix(aggp),dendrogram='row',Colv=NA,trace="none", col=mycol,colCol=ccol[ford],cexRow=0.8, keysize=1.25,symkey=FALSE,symbreaks=FALSE,scale="none", srtCol=90,main="Heatmap of `fs` data.")

#  [1] "#197300"    "#197300"    "#197300"    "#197300"    "#197300"   
#  [6] "#5ed155"    "#5ed155"    "#5ed155"    "#5ed155"    "#5ed155"   
# [11] "#5ed155"    "#660000"    "#660000"    "#660000"    "#cc0000"   
# [16] "#cc0000"    "#cc0000"    "#ff9933"    "#ff9933"    "mediumblue"
# [21] "mediumblue" "mediumblue" "gold"       "gold"

**Figure 2: Heatmap of the cluster means vs channels. Rows and columns are rearranged according to synapse type.**

Percentage of data within cluster is presented on the right side of the heatmap.

2.2 Jittered scatter plot: Lv 0

ggJdat <- stack(dat)
ggD <- data.table(ggJdat)

set.seed(1024)
s2 <- sample(dim(ggD)[1], 5e4)
tmp <- ggD[s2,]
tmp$ind <- as.factor(tmp$ind)
levels(tmp$ind) <- names(feat)[seq(1,144,by=6)][ford]

ggJ0 <- 
  ggplot(data = tmp, aes(x = ind, y = values)) +
  geom_point(alpha=0.75) + 
  geom_jitter(width = 1) + 
  theme(axis.title.x = element_blank()) + 
  theme(axis.text.x = element_text(color = ccol[ford], 
                                   angle=45,
                                   vjust = 0.5))

print(ggJ0)

The above scatter plot is a random sample of the data points.

2.3 Correlations: Lv 0

cmatfs <- cor(fs)
corrplot(cmatfs,method="color",tl.col=ccol[ford], tl.cex=1)

**Figure 4: Correlation on untransformed F0 data, reordered by synapse type.**

3 Level 1: K-means++ for \(K=2\).

We run a Hierachical K-means++ for \(K=2\) on the fs data with 4 levels.

set.seed(2^13)
L <- bhkmpp(dat,blevels=4)

3.1 Heat maps (Lv 1):

## Formatting data for heatmap
aggp <- aggregate(dat,by=list(lab=L[[1]]),FUN=mean)
aggp <- as.matrix(aggp[,-1])
rownames(aggp) <- clusterFraction(L[[1]])

The following are heatmaps generated from clustering via K-means++ (at level 1)

heatmap.2(as.matrix(aggp),dendrogram='row',Colv=NA,trace="none", col=mycol,colCol=ccol[ford],cexRow=0.8, keysize=1.25,symkey=FALSE,symbreaks=FALSE,scale="none", srtCol=90,main="Heatmap of `fs` data.")

#  [1] "#197300"    "#197300"    "#197300"    "#197300"    "#197300"   
#  [6] "#5ed155"    "#5ed155"    "#5ed155"    "#5ed155"    "#5ed155"   
# [11] "#5ed155"    "#660000"    "#660000"    "#660000"    "#cc0000"   
# [16] "#cc0000"    "#cc0000"    "#ff9933"    "#ff9933"    "mediumblue"
# [21] "mediumblue" "mediumblue" "gold"       "gold"

**Figure 5: Heatmap of the cluster means vs channels. Rows and columns are rearranged according to synapse type.**

Percentage of data within cluster is presented on the right side of the heatmap.

3.2 Jittered scatter plot: Lv 1

ggJdat <- stack(dat)
ggD <- data.table(ggJdat)
ggD$label <- L[[1]]

ggCol <- brewer.pal(4,"Set1")[order(table(L[[1]]))]

tmp <- ggD[s2, ]
tmp$label <- as.factor(tmp$lab)
tmp$ind <- as.factor(tmp$ind)
levels(tmp$ind) <- names(feat)[seq(1,144,by=6)][ford]

cf1 <- data.frame(cf = clusterFraction(L[[1]]))

ggJ1 <- 
  ggplot(data = tmp, aes(x = ind, y = values, 
                         color = label)) +
  scale_color_manual(values=ggCol) + 
  geom_point(alpha=0.25, position=position_jitterdodge()) + 
  geom_boxplot(alpha =0.35, outlier.color = 'NA') + 
  annotate("text", x = levels(tmp$ind)[c(2,20)], y = max(tmp$values)+25, 
           label= cf1[1:2,]) + 
  theme(axis.title.x = element_blank()) + 
  theme(axis.text.x = element_text(color = ccol[ford], 
                                   angle=45,
                                   vjust = 0.5))

print(ggJ1)

3.3 Within cluster correlations (Lv 1)

corkp1 <- cor(dat[L[[1]] == 1,])
corkp2 <- cor(dat[L[[1]] == 2,])
difCor12 <- sqrt((corkp1 - corkp2)^2)

layout(matrix(c(1,2,3,3), 4, 2, byrow=TRUE))
corrplot(corkp1,method="color",tl.col=ccol[ford], tl.cex=0.8)
title(sub = "cluster 1")
corrplot(corkp2,method="color",tl.col=ccol[ford], tl.cex=0.8)
title(sub = "cluster 2")
corrplot(difCor12,is.corr=FALSE,method="color",
         tl.col=ccol[ford], tl.cex=0.8, 
         col=colorRampPalette(c("white","white","darkorange"))(50))
title(sub = "cluster difference")

**Figure 7: Within cluster correlations, clock-wise from top left, Cluster 1, Cluster 2, l2 distance between C1 and C2**

Notice that the non-synaptic markers change very little between clusters. Also note that the correlations between (gad, VGAT, PV, Gephyr) and VGlut1 at both times change significantly between clusters.

3.4 Clusters and Spatial Location (Lv 1)

Using the location data and the results of K-means++ we show a 3d scatter plot colored accoding to cluster.

set.seed(2^12)
s1 <- sample(dim(loc)[1],5e4)

locs1 <- loc[s1,]
locs1$cluster <- L[[1]][s1]

plot3d(locs1$V1,locs1$V2,locs1$V3,
       col=brewer.pal(4,"Set1")[order(table(L[[1]]))][locs1$cluster],
       alpha=0.75,
       xlab='x', 
       ylab='y', 
       zlab='z')

subid <- currentSubscene3d()
rglwidget(elementId="plot3dLocations", height=720, width=720)

4 Level 2: K-means++ for \(K=2\).

4.1 Within cluster correlations (Lv 2)

corLV2 <- lapply(c(1:4),function(x){cor(dat[L[[2]] == x,])})

difCor1112 <- sqrt((corLV2[[2]] - corLV2[[1]])^2)
difCor2122 <- sqrt((corLV2[[4]] - corLV2[[3]])^2)

layout(matrix(c(1,2,3,3,4,5,6,6), 4, 2, byrow=TRUE))
corrplot(corLV2[[1]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,1,0))
title("Cluster 1")
corrplot(corLV2[[2]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,1,0))
title("Cluster 2")
corrplot(difCor1112, method="color", tl.col=ccol[ford], 
         tl.cex=0.8,
         mar = c(0,0,1,0),
         cl.lim = c(0,max(difCor1112,difCor2122)),
         col=colorRampPalette(c("white", 
                                "white",
                                "darkorange"))(100))
title("Difference(1,2)")
corrplot(corLV2[[3]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,1,0))
title("Cluster 3")
corrplot(corLV2[[4]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,1,0))
title("Cluster 4")
corrplot(difCor2122, method="color", tl.col=ccol[ford], 
         tl.cex=0.8,
         mar=c(0,0,1,0),
         cl.lim = c(0,max(difCor1112,difCor2122)),
         col=colorRampPalette(c("white", 
                                "white",
                                "darkorange"))(100))
title("Difference(3,4)")

**Figure 8: Within cluster correlations for level 2. (c11, c12, c21, c22)**

4.2 Heat maps (Lv 2):

## Formatting data for heatmap
aggp2 <- aggregate(dat,by=list(lab=L[[2]]),FUN=function(x){mean(x)}) 
aggp2 <- as.matrix(aggp2[,-1])
rownames(aggp2) <- clusterFraction(L[[2]])

The following are heatmaps generated from clustering via K-means++

heatmap.2(as.matrix(aggp2),dendrogram='row',Colv=NA,trace="none", col=mycol,colCol=ccol[ford],cexRow=0.8, keysize=1.25,symkey=FALSE,symbreaks=FALSE,scale="none", srtCol=90,main="Heatmap of `fs` data.")

#  [1] "#197300"    "#197300"    "#197300"    "#197300"    "#197300"   
#  [6] "#5ed155"    "#5ed155"    "#5ed155"    "#5ed155"    "#5ed155"   
# [11] "#5ed155"    "#660000"    "#660000"    "#660000"    "#cc0000"   
# [16] "#cc0000"    "#cc0000"    "#ff9933"    "#ff9933"    "mediumblue"
# [21] "mediumblue" "mediumblue" "gold"       "gold"

**Figure 9: Heatmap of the cluster means vs channels. Rows and columns are rearranged according to synapse type.**

Percentage of data within cluster is presented on the right side of the heatmap.

4.3 Jittered scatter plot: Lv 2

ggJdat <- stack(dat)
ggD <- data.table(ggJdat)
ggD$label <- L[[2]]

ggCol <- brewer.pal(8,"Set1")[order(table(L[[2]]))]

tmp <- ggD[s2, ]
tmp$label <- as.factor(tmp$lab)
tmp$ind <- as.factor(tmp$ind)
levels(tmp$ind) <- names(feat)[seq(1,144,by=6)][ford]

cf2 <- data.frame(cf = clusterFraction(L[[2]]))
ggJ2 <- 
  ggplot(data = tmp, aes(x = ind, y = values, 
                         color = label)) +
  scale_color_manual(values=ggCol) + 
  geom_point(alpha=0.25, position=position_jitterdodge()) + 
  geom_boxplot(alpha =0.35, outlier.color = 'NA') + 
  annotate("text", x = levels(tmp$ind)[c(2,8,14,20)], y = max(tmp$values)+25, 
           label= cf2[1:4,]) + 
  theme(axis.title.x = element_blank()) + 
  theme(axis.text.x = element_text(color = ccol[ford], 
                                   angle=45,
                                   vjust = 0.5))

print(ggJ2)

The fraction of data points within each cluster are given at the top of the plot window. ## Kernel Density Estimates of the marginals | cluster (Lv 2)

Here we look at the kernel density estimates within each cluster to compare.

4.4 Clusters and Spatial Location (Lv 2)

Using the location data and the results of K-means++ we show a 3d scatter plot colored according to cluster.

set.seed(2^12)
s1 <- sample(dim(loc)[1],5e4)

locs2 <- loc[s1,]
locs2$cluster <- L[[2]][s1]

YlOrBr <- c("#FFFFD4", "#FED98E", "#FE9929", "#D95F0E", "#993404")
col.pal <- colorRampPalette(YlOrBr)

plot3d(locs2$V1,locs2$V2,locs2$V3,
       #col=colorpanel(8,"brown","blue")[order(table(L[[2]]))][locs2$cluster],
       col=col.pal(8)[-seq(1,8,2)][order(table(L[[2]]))][locs2$cluster],
       alpha=0.75,
       xlab='x', 
       ylab='y', 
       zlab='z'
       )

subid <- currentSubscene3d()
rglwidget(elementId="plot3dLocationsLV2", height=720, width=720)

5 Level 3: K-means++ for \(K=2\).

5.1 Within cluster correlations (Lv 3)

corLV3 <- lapply(c(1:8),function(x){cor(dat[L[[3]] == x,])})

difCor1 <- sqrt((corLV3[[2]] - corLV3[[1]])^2)
difCor2 <- sqrt((corLV3[[4]] - corLV3[[3]])^2)
difCor3 <- sqrt((corLV3[[6]] - corLV3[[5]])^2)
difCor4 <- sqrt((corLV3[[8]] - corLV3[[7]])^2)
m <- max(difCor1, difCor2, difCor3, difCor4)

layout(matrix(c(1, 2, 3, 3,
                4, 5, 6, 6, 
                7, 8, 9, 9,
                10, 11, 12, 12), 8,2, byrow=TRUE))

corrplot(corLV3[[1]],method="color",tl.col=ccol[ford], tl.cex=0.8,
         mar=c(0,0,1,0))
title('Cluster 1')
corrplot(corLV3[[2]],method="color",tl.col=ccol[ford], tl.cex=0.8,
         mar=c(0,0,1,0))
title('Cluster 2')
corrplot(difCor1,method="color",tl.col=ccol[ford], tl.cex=0.8,
         cl.lim=c(0,m), 
         mar=c(0,0,1,0),
         col=colorRampPalette(c("white","white","darkorange"))(50))
title('Difference(1,2)')
corrplot(corLV3[[3]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,1,0))
title('Cluster 3')
corrplot(corLV3[[4]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,1,0))
title('Cluster 4')
corrplot(difCor2,method="color",tl.col=ccol[ford], tl.cex=0.8, 
         cl.lim= c(0,m),
         mar=c(0,0,1,0),
         col=colorRampPalette(c("white",
                                "white",
                                "darkorange"))(50))
title('Difference(3,4)')
corrplot(corLV3[[5]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,1,0))
title('Cluster 5')
corrplot(corLV3[[6]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,1,0))
title('Cluster 6')
corrplot(difCor3,method="color",tl.col=ccol[ford], tl.cex=0.8,
         cl.lim= c(0,m),
         mar=c(0,0,1,0),
         col=colorRampPalette(c("white",
                                "white",
                                "darkorange"))(50))
title('Difference(5,6)')
corrplot(corLV3[[7]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,1,0))
title('Cluster 7')
corrplot(corLV3[[8]],method="color",tl.col=ccol[ford], tl.cex=0.8, 
         mar=c(0,0,1,0))
title('Cluster 8')
corrplot(difCor4,method="color",tl.col=ccol[ford], tl.cex=0.8,
         cl.lim= c(0,m),
         mar=c(0,0,1,0),
         col=colorRampPalette(c("white",
                                "white",
                                "darkorange"))(50))
title('Difference(7,8)')

**Figure 11: Within cluster correlations for level 3. (c111, c112, c121, c122, c211, c212, c221, c222)**

5.2 Heat maps (Lv 3):

## Formatting data for heatmap
aggp3 <- aggregate(dat,by=list(lab=L[[3]]),FUN=function(x){mean(x)})
aggp3 <- as.matrix(aggp3[,-1])
rownames(aggp3) <- clusterFraction(L[[3]])

The following are heatmaps generated from clustering via K-means++

heatmap.2(as.matrix(aggp3),dendrogram='row',Colv=NA,trace="none", col=mycol,colCol=ccol[ford],cexRow=0.8, keysize=1.25,symkey=FALSE,symbreaks=FALSE,scale="none", srtCol=90,main="Heatmap of `fs` data.")

#  [1] "#197300"    "#197300"    "#197300"    "#197300"    "#197300"   
#  [6] "#5ed155"    "#5ed155"    "#5ed155"    "#5ed155"    "#5ed155"   
# [11] "#5ed155"    "#660000"    "#660000"    "#660000"    "#cc0000"   
# [16] "#cc0000"    "#cc0000"    "#ff9933"    "#ff9933"    "mediumblue"
# [21] "mediumblue" "mediumblue" "gold"       "gold"

**Figure 12: Heatmap of the cluster means vs channels. Rows and columns are rearranged according to synapse type.**

Percentage of data within cluster is presented on the right side of the heatmap.

5.3 Jittered scatter plot: Lv 3

ggJdat <- stack(dat)
ggD <- data.table(ggJdat)
ggD$label <- L[[3]]

ggCol <- brewer.pal(8,"Set1")[order(table(L[[3]]))]

tmp <- ggD[s2, ]
tmp$label <- as.factor(tmp$lab)
tmp$ind <- as.factor(tmp$ind)
levels(tmp$ind) <- names(feat)[seq(1,144,by=6)][ford]

ggJ3 <- 
  ggplot(data = tmp, aes(x = ind, y = values, 
                         color = label)) +
  scale_color_manual(values=ggCol) + 
  geom_boxplot(alpha =0.35, outlier.color = 'NA') + 
  geom_point(alpha=0.25, position=position_jitterdodge()) + 
  #geom_jitter(width=2) + 
  theme(axis.title.x = element_blank()) + 
  theme(axis.text.x = element_text(color = ccol[ford], 
                                   angle=45,
                                   vjust = 0.5))

print(ggJ3)

5.4 Clusters and Spatial Location (Lv 3)

Using the location data and the results of K-means++ we show a 3d scatter plot colored according to cluster.

set.seed(2^12)
s1 <- sample(dim(loc)[1],5e4)

locs3 <- loc[s1,]
locs3$cluster <- L[[3]][s1]

plot3d(locs3$V1,locs3$V2,locs3$V3,
       col=col.pal(16)[-seq(1,8,2)][order(table(L[[3]]))][locs3$cluster],
       alpha=0.65,
       xlab='x', 
       ylab='y', 
       zlab='z'
       )

subid <- currentSubscene3d()
rglwidget(elementId="plot3dLocationsLV3", height=720, width=720)

Synapse Stats: Synapse Exploration

JLP

2016-07-20

1 Kernel Density Estimates of the marginals

2 Level 0

2.1 Heat maps (Lv 0):

2.2 Jittered scatter plot: Lv 0

2.3 Correlations: Lv 0

3 Level 1: K-means++ for \(K=2\).

3.1 Heat maps (Lv 1):

3.2 Jittered scatter plot: Lv 1

3.3 Within cluster correlations (Lv 1)

3.4 Clusters and Spatial Location (Lv 1)

4 Level 2: K-means++ for \(K=2\).

4.1 Within cluster correlations (Lv 2)

4.2 Heat maps (Lv 2):

4.3 Jittered scatter plot: Lv 2

4.4 Clusters and Spatial Location (Lv 2)

5 Level 3: K-means++ for \(K=2\).

5.1 Within cluster correlations (Lv 3)

5.2 Heat maps (Lv 3):

5.3 Jittered scatter plot: Lv 3

5.4 Clusters and Spatial Location (Lv 3)